Verbs classified or not as auxiliaries in various languages

Classifying certain verbs or verbal compounds as auxiliaries, chiefly aspectual and modal ones, can lead to divergent views, more in Romance languages than in Germanic languages , because their grammatical behaviour is about the same as many lexical verbs ( directly followed by an infinitive ). However the question can be also raised about phrases in English as to be likely to , to be able to, to be bound to, to have to and so on. Can they be considered auxiliaries or semi-auxiliaries as modals are called in French, as they give more information on the function of the main verb as tense helping verbs do , but without having the same specific grammatical features. So I am wondering if the Spanish tener que ( Tengo que irme = I have to go ) which has about the same meaning and function as the modal deber ( must ) ( Debe trabajar = He/She must work ) may not be put in the sam class.
And what about impersonal forms as Hay que comer para vivir / Il faut manger pour vivre / 'One must eat to live' ? I suppose such expressions cannot be considered auxiliaries due to the construction; do you agree ? .